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Sidana [21]
3 years ago
15

156 students at summer camp There are 13 cabins an equal number of students sleep in each cabin how many students stay in each c

abin
Mathematics
1 answer:
lions [1.4K]3 years ago
6 0

Answer:

12

Step-by-step explanation:

if you divide 156 students into 13 cabins you divide it into equal groups, once you divide all of it to equal groups you get 12 students in each cabin.

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In ΔABC, if AB = 14 and BC = 9, AC may be equal to
Pie

Answer:

AC could be any number of these numbers 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

Step-by-step explanation:

There is a fact in any triangle:

<em>The length of any side of a triangle must be greater than the difference of the lengths of the other two sides and smaller than the sum of the lengths of the other two sides</em>

If the lengths of the three sides of a triangle are a , b and c, then

  • a - b < c < a + b
  • b - c < a < b + c
  • a - c < b < a + c

In Δ ABC:

→ (BC) - (AC) < AB < (BC) + (AC)

→ (AB) - (AC) < BC < (AB) + (AC)

→ (AB) - (BC) < AC < (AB) + (BC)

∵ AB = 14 units

∵ BC = 9 units

- Find the sum and difference of them

∵ AB - BC = 14 - 9

∴ AB - BC = 5

∵ AB + BC = 14 + 9

∴ AB + BC = 23

- That means the length of AC could be any integer greater

    than 5 and smaller than 23

∴ 5 < AC < 23

AC could be any number of these numbers 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

5 0
3 years ago
Read 2 more answers
The center of an ellipse is (-9,3). one focus is (-7,3). The major axis is 24 units long. What is the equation of the ellipse in
CaHeK987 [17]

Answer:

\frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1

Step-by-step explanation:

The standard equation of the ellipse is

\frac{(x-\alpha)^2}{a^2}+\frac{(y-\beta)^2}{b^2}=1\;\cdots(i)

where, (\alpha, \beta) is the center and a,b are semi axes of the ellipse along x-axis and y-axis respectively.

Given that, (\alpha, \beta)=(-9,3) and major axis, 2a=24.

So, semi major axis, a=24/2=12.

Now, focus of the ellipse is (-7,3).

Let e be the eccentricity of the ellipse,

So, e=\frac c a

where c is the distance between the center and focus of the ellipse.

By using the distance formula,

c=\sqrt{(-9-(-7))^2+(3-3)^2}=2

\Rightarrow e=\frac {2}{12}=\frac{1}{6}\;\cdots(ii)

Again, the relationship among a,b and e is

e=\sqrt{1-\frac{b^2}{a^2}

\Rightarrow \frac{1}{6}=\sqrt{1-\frac{b^2}{(12)^2} [from equation (ii)]

\Rightarrow \frac{1}{36}=\sqrt{1-\frac{b^2}{144} [squaring on both the sides]

\Rightarrow \frac{b^2}{144}=1-\frac{1}{36}

\Rightarrow b^2=\frac{35}{36}\times144=140

So, the value of square of semi-minir axis, b^2=140.

Hence, from equation (i), the equation of required ellipse is standard form is

\frac{(x-(-9))^2}{144}+\frac{(y-3)^2}{140}=1

\Rightarrow \frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1

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3 years ago
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Nastasia [14]
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3 years ago
Graph f(x) = x and g(x) =<br> and g(x) =-1/3x+2<br> x on the same coordinate plane.
Kay [80]

Hey there!

Let's think of both of these functions as two different slope-intercept equations (y=mx+b). Don't let all of the fs and gs confuse you; those are just showing that they are two different functions!

Our function f has an equation of y=x, which is a diagonal line that passes through the origin and goes across each small grid on the graph diagonally.

Our function g has an equation of y=-1/3x+2, which means that it will intersect with the y-axis at two units above the origin and for every three whole steps it goes to the right, it will have gradually gone down one whole step as well.

Attached to my answer is what a graph of it would kind of look like. Sorry if the lines don't look too much like a line it's a bit difficult to draw with a mouse haha!

I hope that this helps! Have a wonderful day!

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4 years ago
Cup of juice. Howard mixes 1 2/3 cups of water with 1/4 cup juice. Whose mixture is stronger
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Is there more to the question??
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